c-numerical range of operator products on B(H)

Abstract: Let H be a complex Hilbert space of dimension no less than 2 and B(H) be the algebra of all bounded linear operators on H. We give the form of surjective maps on B(H) preserving c-numerical range of operator products when the maps satisfy preserving weak zero products. As a result, we obtain the characterization of surjective maps on Mn(C) preserving c-numerical range of operator products. The proof of the results depends on some propositions of operators in B(H), which are of different interest.